ACEEE Int. J. on Communication, Vol. 02, No. 01, Mar 2011
A Sensitive WaveletBased Algorithm for Fault
Detection in Power Distribution Networks
N. Zamanan M. Gilany
College of Technological Studies,
Dept. of Electrical Engineering,
Kuwait
W. Wahba
Faculty of Engineering,
Faoum University,
Egypt
Abstract — This paper presents a wavelet based technique for
detection and classification of abnormal conditions that occur
on power distribution lines. The transients associated with these
conditions contain a large spectrum of frequencies, which are
analyzed using wavelet transform approach. The proposed
technique depends on a sensitive fault detection parameter
(denoted SFD) calculated from wavelet multiresolution
decomposition of the three phase currents. The simulation
results of this study clearly indicate that the proposed technique
can be successfully used to detect not only faults that could not
be detected by conventional relays but also abnormal transients
like load switching and inrush currents.
Keywords — Wavelet Transform, Fault detection, Distribution
Networks, Inrush currents.
I.Introduction
Power disturbance occur due to changes in the
electrical configurations of a power circuit. Disturbance
causing failure are infrequent compared to the number of
disturbances that occur every day due to normal system
operations (switching of lines, switching on/off generating
units, or switching of capacitor banks to balance inductive
loads). In order to improve electrical power quality, one must
have the ability to detect and classify these disturbances.
There are two main problems related to protection of
distribution networks.
1. The first problem is the faults through high resistance.
These faults are not easy to be detected, since the fault
current may not reach the setting of the relay. It may
cause successive heating and fires unless the fault is
isolated.
2. The second problem is the numerous cases of power
system transients (like switching) which may cause
transient responses similar to that induced by the
permanent faults. It is hence necessary to identify the
disturbance type and classify it in order to have a high
reliability levels.
The waveforms associated with these transients are
typically nonperiodic signals, which contain both high
frequency oscillations and localized impulses superimposed
on the power frequencies. In order to extract or separate these
©2011 ACEEE
DOI: 01.IJCom.02.01.180
superimposed signals, several algorithms have been
introduced in power system such as Kalman filtering, least
square method, and Fourier transform. However, in presence
of nonstationary signals, the performance of these
algorithms is limited and this is the introduction to the need
of wavelet transform (WT).
The idea of application of wavelet transform analysis to
fault detection in power systems is not new and there are
hundreds of publications related to this idea. The wavelet
based techniques are applied in different power system
applications such as detecting arcing faults in distribution
systems [1], locating SLG faults in distribution lines [2],
stator ground fault protection schemes with selectivity for
generators [3], locating faults in transmission systems [4,5],
locating faults in systems with tapped lines [6] and solving
inrush current problems [7,8].
Application of wavelet transform in protection of
distribution networks faces two main difficulties that have
limited the usefulness of these techniques. The first difficulty
is that the transient levels in distribution circuits are generally
small compared with that in HV transmission networks. The
second difficulty faces the application of wavelet transforms
in protection of distribution networks is the need to add extra
components (e.g. VTs) to the existing distribution protection
systems in order to apply such techniques. Analyzing voltage
waveforms is much easier than current waveforms due to
the large content of harmonics in voltage waveforms. Most
researchers are using both current and voltage samples of
the three phases as inputs for fault detection in order to
overcome this difficulty [1,2,3,6,7,8]. However, many
distribution systems are not provided with voltage
transformers since they are using overcurrent relays. Other
researchers use extra hardware like GPS to improve the
usefulness of these techniques [6, 9].
A sensitive parameter (denoted SFD) is used in this paper
to detect and classify faults in distribution networks under
different operating conditions including lowcurrent faults
and arcing faults. The technique can also be used to
discriminate between the transients due to switchingon
additional loads and that due to 3LG faults through high
resistance. In all cases, the proposed technique is not affected
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ACEEE Int. J. on Communication, Vol. 02, No. 01, Mar 2011
with the above mention two limitations (low harmonic
contents or need for voltage signals). It also discriminates
between the inrush currents and fault currents. In the next
section, a theoretical background of wavelet theory is
reviewed. The proposed algorithm and the simulation results
are then presented in the subsequent sections.
II.Theoretical Background
In order to extract certain information from a given signal,
mathematical transformations are required. WT is very well
suited for wideband signals that are not periodic and may
contain both sinusoidal and impulse transients, as is typical
in power system transients. In particular, the ability of
wavelets to focus on shorttime intervals for high frequency
components and longtime intervals for low frequency
components improves the analysis of signals with localized
impulses and oscillations, particularly in the presence of
fundamental and loworder harmonics [9].
The Wavelet Transform (WT) of a continuous time domain
signal f(t) is defined as:
dt (1)
Where a is the scale constant (dilation) and b is the
translation constant (time shift). The 0(t) is the wavelet
function that is short, oscillatory with zero average and
decays quickly at both ends. This property of 0(t) ensures
that the integral in equation (1) is finite and that is why the
name wavelet or "small wave" is assigned to the transform.
The term 0(t) is referred to as the "mother wavelet" and its
dilates (a) and translates (b) simply are referred to as "
wavelets".
Wavelets have a window that is automatically adapted to
give an appropriate resolution. The window is shifted along
the signal and for every position the spectrum is calculated.
This process is repeated many times with a slightly shorter
(or longer) window for every new cycle. At the end of this
process, the result will be a collection of timefrequency
representations of the signal, all with different resolutions.
Because of this collection of representations we can speak
of a multiresolution analysis (MRA) [10].
The wavelet transform given by Eq. (1) has a digital
counterpart known as the Discrete Wavelet Transform
(DWT). The DWT is defined as
Dm(f,m,n)=f=Yf(kyr
V^O k
nka^
(2)
where the parameters a and b in Eq. (1) are replaced by a™
and (ka™ ). The parameters k and m are integer variables.
The actual implementation of the DWT involves
successive pairs of highpass and lowpass filters at each
scaling stage of the wavelet. The successive stages of
decomposition are known as levels or details (denoted
detail_l or dl for short, detail_2 or d2 for short, etc.). The
multiresolution analysis, MRA details at various levels
contain the features that can be used for detection and
classification of faults. More details about wavelet transform
can be found in [1112].
The choice of mother wavelet, 0(t) plays a significant
role in detecting and localizing different types of fault
transients. Each mother function has its own features
depending on the application requirements. The proposed
technique is depending on detecting and analyzing low
amplitude, short duration, fast decaying high frequency
current signals. In this study, Daubechies wavelets (D4) is
chosen since it is effective for the detecting fast and short
transient disturbances [13].
III.The Proposed Algorithm
In the proposed technique, the wavelet transform is firstly
applied to decompose the three phase current signals into a
series of detailed wavelet components, each of which is a
time domain signal that covers a specific frequency band,
hence the time and frequency domains features of the
transient signals are extracted.
Wavelet analysis involves selection of an appropriate
wavelet function called "mother wavelet". The choice of
mother wavelet plays a significant role in detecting and
localizing different types of fault transients. Each mother
function has its feasibility depending on the application
requirements. In this study we are interested in detecting
and analyzing low amplitude, short duration, fast decaying
and oscillating type of high frequency current signals. One
of the most popular mother wavelets suitable for such
applications is the daubichies's wavelet. In this paper, D4
wavelet is used for the analysis of the current waveforms.
For each cycle, the detail signals dl and d2 of each of the
threephase currents are calculated. The sensitive fault
detection parameter used in this work, SDF is a moving
average filter for the summation of the squared of dl and d2
of the three phase currents. Involving only two levels details
ensures less computational burden and fast speed. This
parameter is calculated as follows:
SFD p (k) = SFD p (k 1)+ i///(A)i d p 2 (kn),
!j=1
f!=l
pe(a.b.c)
(3)
where n is the number of samples in the window, h
is the suffix for the detail order (1 or 2 ) and p = (a, b, c) are
suffixes used for phases.
A fault is detected if the value of SFD exceeds a
threshold setting (equal to 300 in this study). This threshold
is selected according to the detail values in normal and fault
operations. The previouslymentioned limitations for
applying wavelet in distribution networks are reduced in the
© 2011 ACEEE
DOI: Ol.IJCom.02.01.180
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iVACEEE
ACEEE Int. J. on Communication, Vol. 02, No. 01, Mar 2011
proposed technique for the two following reasons:
The proposed technique concentrates on the noise
frequency of the signal not on the noise amplitude. The
proposed technique uses the parameter SFD over one cycle
of the current signal which is very sensitive to any small
changes in the current signal since it uses the squared of the
first and second details of the decomposed signals.
IV.MODELING OF POWER SYSTEM
The power system under study was modeled using the
Matlab power system toolbox. Simulations for fault analysis
are carried out on the low voltage side of a 66/11 KV
transformer connected to two 20 kmfeeders. The 20 km
overhead feeder is modeled using the distributed parameters.
A sampling rate of 20 kHz is used, which covers the range
of frequencies from 10 kHz to DC. To prove the sensitivity
of the proposed technique, all the simulation studies are done
with fault current magnitudes lower than the typical
overcurrent relay settings. Some fault cases are carried out
with a fault current lower than the normal load current. Only
the three phase current signals are used in order to avoid
adding extra components (voltage transformers) to the typical
existing protection system in distribution networks.
V. Simulation Results
Intensive simulations for a large number of case
studies were carried out, taking into consideration different
normal and abnormal conditions. The simulation study using
Matlab is adopted to generate the current signals of the power
system under study. The current signals are then decomposed
into different levels of frequencies. The SFD (given in A 2 ) is
calculated using only detail_l and detail_2 for each phase.
The predetermined threshold is compared to the calculated
SFD and accordingly, the fault is detected and classified.
The performance of the proposed technique under different
conditions is illustrated in the following sub sections.
A. High resistive SLG faults
In this case, a SLG fault is simulated at a distance
of 10 km. The fault resistance is chosen, such that the fault
current does not exceed 200% of the rated load current. This
is the typical pickup setting for ordinary overcurrent relays.
The details (dl and d2) of the faulty phase current is shown
in Fig. 1, where that of a healthy phase (phaseB as an
example) are shown in Fig. 1.
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5a ~q « I
Fig. 1: Detail_l and detail_2 for the faulty phase (SLG fault)
The waveforms of the healthy phases may contain
high frequency signals due to mutual coupling as shown in
Fig. 2. The SFD of the healthy phase is very small compared
to that of the faulty phase as shown in Fig. 3.
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Fig. 2: Detail_l and detail_2 for a healthy phase (SLG fault).
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Fig. 3 : The SFD for the faulty and a healthy phase for a SLG
fault.
B.
High resistive 3 LG fault
In this case, a (3LG) fault is considered. To add
more difficulties to this fault case, it is assumed that the fault
occurred near to the far end of the feeder (at a distance of 1 8
km from the sending end). The inception angle is 120°. The
three phase currents are shown in Fig. 4. The corresponding
wavelet details for one of the three faulty phases are shown
in Fig. 5.
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2000 
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Fig. 4: The three phase currents for 3LG fault.
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Fig. 5: The decomposition for one of the three phase currents (for
3LG fault).
The SFD for this case is shown later in Fig 7(a2,
b2, c2) in order to be compared with the case presented in
the next subsection (switching on additional load).
C. Load switching
Transients may be initiated due to switching opera
tions e.g. when adding a new load to the system. Discrimi
nation between the transients generated due to switching con
dition and that due to faults is of great importance. Figure 6
shows the waveforms of the three phase currents during
switching condition. The inception angle was chosen to be
120° to create some sort of analogy between this switching
condition and the case presented in the previous section (3LG
fault).
©2011 ACEEE
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■k ACEEE
ACEEE Int. J. on Communication, Vol. 02, No. 01, Mar 2011
°1000.0 !
2000.0 J
Samples
Fig. 6: Three phase currents for load switching
The similarity between the two cases is more critical if
the low frequency signals are considered, and hence, a false
trip may not be avoided. The proposed technique avoids this
problem since the proposed technique uses only the high
frequency signals (details 12 only).
The SFD of these frequency bands (shown in Fig. 7(al,
bl, cl)) are less than the predetermined threshold, therefore
such cases will be recognized as switching conditions and
not fault conditions since all of the SFDs exceeds the
threshold (Threshold = 300).
a MM .
SX ,
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al. SFD (load switching)
a2. SFD (3LG fault)
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bl. SFD (load s v. itching)
J3Z SFD (3LG fault)
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Fig. 7: A Comparison between the SFD for 3LG fault and the SFD
for load switching
Discrimination between Permanent Faults and
Inrush currents
When a transformer is switched off, its core gener
ally retains some residual flux. Later, when the transformer
is reenergized, the core is likely to saturate. If it does, the
primary windings draw large magnetizing currents from the
power system. This phenomenon is known as magnetizing
inrush and is characterized by the transformer drawing large
currents from the source but supplying relatively smaller
currents to the loads. This results in a large differential cur
rent which causes differential relay to operate. But it is not a
fault condition, and therefore the relay must be able to dis
criminate inrush current from internal fault current, and re
main stable during inrush current.
To date, there are many discrimination methods
[7,8,14,15]. Each of these methods has its own shortcoming.
For the second harmonic restrained method, under some
special conditions, such as when the power transformer is
connected to a long transmission line, or when the current
transformer (CT) is saturated, the second harmonic
component of the transformer current will increase, thereby
affecting the operation of the relay.
In this paper, the sensitive SFD parameter is examined
against this problem. The results show that tracing the value
of this parameter gives an excellent index for the
discrimination between the permanent faults and inruch
currents as shown in the following results.
The inrush condition is simulated at different inception
angles to almost cover all possible inrush current waveforms.
Figure 8 shows the waveforms of one of the phase currents
( IA). The inception angle is assumed to be zero. The
decomposed signals (details) of the discrete wavelet
transform are shown in Fig. 9.
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Fig. S^ A typical inrush current case
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9. Detaill and detail_2 for inrush current in phaseA with zero inception
angle.
The existence of the higher frequency signals
superimposed on the fundamental can clearly demonstrated
by wavelet transform. In this study, details 12 are only the
ones employed in the analysis and feature extraction. For
inrush condition, the high frequencies are of small magnitude
compared with low frequencies. This feature is so important
in the discrimination between internal faults and inrush
currents. The value of SFD for all the examined cases are
will below the setting threshold value as shown in Fig. 10.
© 2011 ACEEE
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ACEEE Int. J. on Communication, Vol. 02, No. 01, Mar 2011
300 n
200 ■
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VI.CONCLUSIONS
Distribution feeders are subjected to all types of
faults. Detection of these faults and discriminating it from
other transient conditions such as switching is of great
importance. These faults can occur through resistances, that
make the fault current not in the range of the setting of
conventional relays and hence the fault will be not easy to
be detected. The use of wavelet transform with the proposed
sensitive SFD parameter makes it easy not only to detect the
occurrence of a fault and its type but also to discriminate
between transients due to switching conditions/inrush
currents and that due to faults. A subroutine is designed to
detect arcing faults in which the level of fault current is very
small. Lots of simulation results show that the proposed
method can exactly and effectively detect and classify both
normal and abnormal conditions in the distribution networks.
Acknowledgments
The financial support from the PAAET in Kuwait (Project
No. TS0902 ) is highly appreciated.
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